Estimation of non-symmetric and unbounded region of attraction using shifted shape function and R-composition

Dongyang Li; Dmitry Ignatyev; Antonios Tsourdos; Zhongyuan Wang

doi:10.1016/j.isatra.2022.11.015

Estimation of non-symmetric and unbounded region of attraction using shifted shape function and R-composition

ISA Trans. 2023 May:136:308-322. doi: 10.1016/j.isatra.2022.11.015. Epub 2022 Nov 21.

Authors

Dongyang Li¹, Dmitry Ignatyev², Antonios Tsourdos², Zhongyuan Wang³

Affiliations

¹ School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield MK43 OAL, UK. Electronic address: dongylee@njust.edu.cn.
² School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield MK43 OAL, UK.
³ School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China.

PMID: 36503619
DOI: 10.1016/j.isatra.2022.11.015

Abstract

Sum-of-squares programming is widely used for region of attraction (ROA) estimations of asymptotically stable equilibrium points of nonlinear polynomial systems. However, existing methods yield conservative results, especially for non-symmetric and unbounded regions. In this study, a cost-effective approach for ROA estimation is proposed based on the Lyapunov theory and shape functions. In contrast to existing methods, the proposed method iteratively places the center of a shifted shape function (SSF) close to the boundary of the acquired invariant subset. The set of obtained SSFs yields robust ROA subsets, and R-composition is employed to express these independent sets as a single but richer-shaped level set. Several benchmark examples show that the proposed method significantly improves ROA estimations, especially for non-symmetric or unbounded ROA without a significant computational burden.

Keywords: Lyapunov stability; Non-symmetric and unbounded region of attraction; Polynomial nonlinear system; Shape function; Sum of squares programming.